@inproceedings{ duchier-fg2009,
code = {(i)},
title = {{A} model-theoretic framework for grammaticality judgements},
booktitle = {{C}onference on {F}ormal {G}rammar ({F}{G}2009)},
author = {Denys Duchier and Jean-Philippe Prost and Thi-Bich-Hanh Dao},
month = jun,
url = {http://hal.archives-ouvertes.fr/hal-00458937/en/},
pages = {1-14},
year = {2009},
aeres = {ACTI},
abstract = {Although the observation of grammaticality judgements is well acknowledged, their formal representation faces problems of different kinds{:} linguistic, psycholinguistic, logical, computational. In this paper we focus on addressing some of the logical and computational aspects, relegating the linguistic and psycholinguistic ones in the parameter space. We introduce a model-theoretic interpretation of Property Grammars, which lets us formulate numerical accounts of grammaticality judgements. Such a representation allows for both clear-cut binary judgements, and graded judgements. We discriminate between problems of Intersective Gradience (i.e., concerned with choosing the syntactic category of a model among a set of candidates) and problems of Subsective Gradience (i.e., concerned with estimating the degree of grammatical acceptability of a model). Intersective Gradience is addressed as an optimisation problem, while Subsective Gradience is addressed as an approximation problem.}}